You’re more at risk of damaging the power supply, tbh. If the volts match, you won’t damage the circuits on your device. But amp ratings on power supplies are primarily concerned with heat dissipation. Amps are pulled by the device, not pushed by the supply. So when the device pulls more amps than the supply is rated for, the supply will potentially overheat. Because you’re forcing the supply to provide more power than it is rated for, which is potentially generating more heat than it is rated to dissipate.
But most decent manufacturers will slightly under-rate their power supplies for safety purposes. So a 3A supply may be capable of dissipating 3.5A (or more) of heat. Best case scenario, the supply gets a little warm. But in the worst case scenario, you melt the supply start a fire.
Many modern charging solutions (like USB-C and electric vehicle chargers) require devices to perform a “handshake” before power is supplied. This handshake basically has the device and power supply trade business cards, so the device knows how much power the supply is capable of providing, and the charger knows how much power the device will potentially need. And if the handshake fails, then the devices simply fall back to lower amperage “slow” charging. But this is only true for more recent connectors like USB-C. Older connectors (like microUSB) don’t require this. The supply might have a current limiter, but it might not. If it doesn’t, it’ll overheat.
Worth noting that in some edge cases, the voltage may begin to drop if the supply isn’t able to keep up with the power demands. While it won’t break the device, it could lead to erratic behavior. CPUs don’t typically like being under voltaged, and it can cause errors or crashes if the voltage dips. Turning down your system clock could potentially help avoid these crashes, since a slower system clock will use less power. But this will obviously slow your device down. So it’s a trade-off that you’ll need to consider.